c8 Use the data in DISCRIM.RAW to answer this question. These are ZIP code–level data on prices for various items at fast-food restaurants, along with characteristics of the zip code population, in New Jersey and Pennsylvania. The idea is to see whether fast-food restaurants charge higher prices in areas with a larger concentration of blacks.

(i)       Find the average values of prpblck and income in the sample, along with their standard deviations. What are the units of measurement of prpblck and income?

(ii)      Consider a model to explain the price of soda, psoda, in terms of the proportion of the population that is black and median income:

 

psoda 5 b0 1 b1prpblck 1 b2income 1 u.

Estimate this model by OLS and report the results in equation form, including the sample size and R-squared. (Do not use scientific notation when reporting the esti- mates.) Interpret the coefficient on prpblck. Do you think it is economically large?

(iii)    Compare the estimate from part (ii) with the simple regression estimate from psoda on prpblck. Is the discrimination effect larger or smaller when you control for income?

(iv)    A model with a constant price elasticity with respect to income may be more appropriate. Report estimates of the model

 

log(psoda) 5 b0 1 b1prpblck 1 b2log(income) 1 u.

If prpblck increases by .20 (20 percentage points), what is the estimated percent- age change in psoda? (Hint: The answer is 2.xx, where you fill in the “xx.”)

(v)     Now add the variable prppov to the regression in part (iv). What happens to bˆprpblck?

(vi)    Find the correlation between log(income) and prppov. Is it roughly what you expected?

(vii)  Evaluate the following statement: “Because log(income) and prppov are so highly correlated, they have no business being in the same regression.”